The signals from digital electrical engineering are modeled by discrete time and real time functions, whose values are binary n-tuples and which are also called signals. The asynchronous circuits, representing the devices that work with such signals, are modeled by Boolean autonomous deterministic regular asynchronous systems, shortly by asynchronous flows. The attribute Boolean' vaguely refers to the binary Boole algebra; autonomous' means that there is no input; deterministic' means the existence of a unique state function; and regular' indicates the existence of a Boolean function that iterates its coordinates independently on each other (ie: asynchronously). Strong analogies exist with the real, usual dynamical systems. The purpose of this research monograph is to study the periodicity of the signals and of their values, as well as the periodicity of the asynchronous flows. The monograph addresses systems theory and computer science that apply to researchers, but it is also interesting to those that study periodicity itself. From this last perspective, the signals may be thought of as functions with many finite values. At the same time, the asynchronous flows may be considered as special cases of variable structure systems. The bibliography consists of works of real, dynamical systems that produce analogies.